{
  "id": "1711.07152",
  "version": "v1",
  "published": "2017-11-20T05:30:15.000Z",
  "updated": "2017-11-20T05:30:15.000Z",
  "title": "On $e$-positivity and $e$-unimodality of chromatic quasisymmetric functions",
  "authors": [
    "Soojin Cho",
    "JiSun Huh"
  ],
  "comment": "22pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The $e$-positivity conjecture and the $e$-unimodality conjecture of chromatic quasisymmetric functions are proved for some classes of natural unit interval orders. Recently, J. Shareshian and M. Wachs introduced chromatic quasisymmetric functions as a refinement of Stanley's chromatic symmetric functions and conjectured the $e$-positivity and the $e$-unimodality of these functions. The $e$-positivity of chromatic quasisymmetric functions implies the $e$-positivity of corresponding chromatic symmetric functions, and our work resolves Stanley's conjecture on chromatic symmetric functions of $(3+1)$-free posets for two classes of natural unit interval orders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-20T05:30:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05C15",
      "05C25"
    ],
    "keywords": [
      "positivity",
      "natural unit interval orders",
      "unimodality",
      "chromatic quasisymmetric functions implies",
      "work resolves stanleys conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}